M7Unit 5

Name of Number System	Symbol of Number System	Definition of Number System	The Set of numbers in this number system.
Natural Numbers	N	The counting numbers.	{1, 2, 3,…}
Whole Numbers	W	The counting numbers and zero.	{0, 1, 2, 3,… }
Integers	I	The counting numbers, their additive inverses and zero.	{…, -3, -2, -1, 0, 1, 2, 3, …}
Rational Numbers	Q	Any number of the form a/b where a and b are integers and b ¹ 0.

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Coordinate Plane – Cartesian Plane

When describing an point on the plane we use ordered pairs. In an ordered pair you always give the x-coordinate first and the y-coordinate second. Points are often labeled, we use capital letters to label points.

Example: A(5,3)

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Opposites

To find the opposite of an integer you change the sign.

Examples:

The opposite of (+1) is (-1). The opposite of (-346) is (+346).

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Absolute value

Every positive and negative integer has a sign and an absolute value. The absolute value of an integer is the value of the integer without regard to the sign. The symbol for absolute value is two vertical line segments. Sometimes the absolute value of an integer is called its magnitude.

| 1 | = 1 |-1| = 1 - this is the number of units a number is from zero on a number line.

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Operations on Integers

Addition

When adding integers there are two situations to consider:

The signs are the same - add the numbers and give that sign.

Examples:

(+5) + (+6) = (+11) (-5) + (-6) = (-11)

The signs are different - subtract the numbers and give the sign of the number with the largest absolute value.

Examples:

(-5) + (+6) = (+1) (+5) + (-6) = (-1)

Subtraction

When subtracting integers we add the opposite.

Examples:

(+5) - (+3) (+5) - (-3) (-5) - (+3) (-5) - (-3)

(+5) + (-3) (+5) + (+3) (-5) + (-3) (-5) + (+3)

(+2) (+8) (-8) (-2)

Multiplication & Division

When multiplying and dividing integers there are two situations to consider.

The signs are the same - then the answer is positive.

Examples:

(+3) x (+2) (-3) x (-2) (+8) ¸ (+4) (-8) ¸ (-4)

(+6) (+6) (+2) (+2)

The signs are different - then the answer is negative.

Examples:

(+3) x (-2) (-3) x (+2) (+8) ¸ (-4) (-8) ¸ (+4)

(-6) (-6) (-2) (-2)

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Order of Operations

B brackets

E exponents

M division & multiplication in order from left to right

S addition & subtraction in order from left to right

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Relations

A Relation is an association between two quantities in a definite order, as specified by a relation rule, usually in the form of an equation.

Mapping shows the relation between the two sets.

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Function Charts

Function charts can be used to show input-output and to generate ordered pairs.

x ® 2x
1	2
2	4
3	6

m ® m+3
0	3
1	4
2	5
3	6
4	7
5	8

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Problem Solving

5 step problem solving method. Example:

A spacecraft countdown is at –8s. In how many seconds will the spacecraft be 15 s into its flight?

F: s = - 8s

f = 15 s

Q: c = ?

P: c = f – s

W: ? = 15 – (-8)

? = 15 + 8

? = 23

S: In 23 seconds the spacecraft will be 15s into its flight.

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Internet Sites

	Positive and Negative Numbers - a summary of where and how we use positive and negative numbers
	Addition and Subtraction of Positive and Negative Numbers - shows how to use a number line to add & subtract Integers
	Multiplication of Positive and Negative Numbers - shows how to use a number line to multiply Integers
	Division of Positive and Negative Numbers - shows how to use a number line to divide Integers
	Order of Operations - review of order of operations
	Exponents - review of what exponents do
	Working With Signed Numbers Review - review on order of operations and adding, subtracting, multiplying, and dividing signed numbers
	Drawing Plane and Coordinate System - different applets so you can plot points on a coordinate plane
	The Cartesian Plane
	The Cartesian Plane - a summary and explanation on how to plot points
	The Coordinate Plane - an explanation and description of the basics
	Coordinate Geometry - lessons in coordinate geometry
	Positive and Negative Numbers - a summary of Integers
	Absolute Value
	Math A: Absolute Value
	Mrs. Glosser's Math Goodies: Integers
	Integers
	Signed Integers
	Integers: Operations with Signed Numbers
	Mystery Picture Game
	Operations on Integers
	Integers Menu
	Comparing Integers
	Subtracting Negative and Positive Integers
	Interesting Integers
	Adding and Subtracting Integers Gizmo
	Colour Chips Addition - this is a site that uses positive and negative tiles
	Colour Chips Subtraction - this is a site that uses positive and negative tiles
	Math: Integers - a site with several interactives
	What's the Point - game
	Line Jumper
	Operation Order

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	Number Systems
	Coordinate Plane – Cartesian Plane
	Opposites
	Absolute value
	Operations on Integers
	Order of Operations
	Relations
	Function Charts
	Problem Solving
	Internet Sites